Driving on a tilt road is a section optimal for a fuel operation due to an increase in acceleration. In this case, it is possible to actively and rapidly enter a fuel cut mode in consideration of RPM and a tilt angle. The related art has proposed various components for reducing fuel of a vehicle in the inclined road. One of components that have been proposed in the related art is a tilt sensitive fuel cut valve. The component is a ball value that is sensitive to a tilt of a vehicle so as to be displaced from a valve opening position to a valve closing position. The ball valve cuts a supply of fuel from a fuel tank to a fuel injection device. However, the component starts and releases a fuel cut by using only a vehicle tilt angle due to a mechanical configuration and does not reflect driving habit or acceleration intention of a driver, which cannot improve convenience of driving.